{
 "metadata": {
  "name": ""
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Set up "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import pylab\n",
      "pylab.rcParams['xtick.major.pad']='8'\n",
      "pylab.rcParams['ytick.major.pad']='8'\n",
      "#import matplotlib.gridspec as gridspec\n",
      "from matplotlib import rc\n",
      "rc('text', usetex=False)\n",
      "rc('font', family='serif')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from os import listdir\n",
      "files = listdir('.')\n",
      "if 'blackouts.txt' not in files:\n",
      "    import urllib\n",
      "    urllib.urlretrieve('https://raw.github.com/jeffalstott/powerlaw/master/manuscript/blackouts.txt', 'blackouts.txt')\n",
      "if 'words.txt' not in files:\n",
      "    import urllib\n",
      "    urllib.urlretrieve('https://raw.github.com/jeffalstott/powerlaw/master/manuscript/words.txt', 'words.txt')\n",
      "if 'worm.txt' not in files:\n",
      "    import urllib\n",
      "    urllib.urlretrieve('https://raw.github.com/jeffalstott/powerlaw/master/manuscript/worm.txt', 'worm.txt')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from numpy import genfromtxt\n",
      "blackouts = genfromtxt('blackouts.txt')#/10**3\n",
      "words = genfromtxt('words.txt')\n",
      "worm = genfromtxt('worm.txt')\n",
      "worm = worm[worm>0]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def plot_basics(data, data_inst, fig, units):\n",
      "    from powerlaw import plot_pdf, Fit, pdf\n",
      "    annotate_coord = (-.4, .95)\n",
      "    ax1 = fig.add_subplot(n_graphs,n_data,data_inst)\n",
      "    plot_pdf(data[data>0], ax=ax1, linear_bins=True, color='r', linewidth=.5)\n",
      "    x, y = pdf(data, linear_bins=True)\n",
      "    ind = y>0\n",
      "    y = y[ind]\n",
      "    x = x[:-1]\n",
      "    x = x[ind]\n",
      "    ax1.scatter(x, y, color='r', s=.5)\n",
      "    plot_pdf(data[data>0], ax=ax1, color='b', linewidth=2)\n",
      "    from pylab import setp\n",
      "    setp( ax1.get_xticklabels(), visible=False)\n",
      "    #ax1.set_xticks(ax1.get_xticks()[::2])\n",
      "    ax1.set_yticks(ax1.get_yticks()[::2])\n",
      "    locs,labels = yticks()\n",
      "    #yticks(locs, map(lambda x: \"%.0f\" % x, log10(locs)))\n",
      "    if data_inst==1:\n",
      "        ax1.annotate(\"A\", annotate_coord, xycoords=\"axes fraction\", fontsize=14)\n",
      "\n",
      "    \n",
      "    from mpl_toolkits.axes_grid.inset_locator import inset_axes\n",
      "    ax1in = inset_axes(ax1, width = \"30%\", height = \"30%\", loc=3)\n",
      "    ax1in.hist(data, normed=True, color='b')\n",
      "    ax1in.set_xticks([])\n",
      "    ax1in.set_yticks([])\n",
      "\n",
      "    \n",
      "    ax2 = fig.add_subplot(n_graphs,n_data,n_data+data_inst, sharex=ax1)\n",
      "    plot_pdf(data, ax=ax2, color='b', linewidth=2)\n",
      "    fit = Fit(data, xmin=1, discrete=True)\n",
      "    fit.power_law.plot_pdf(ax=ax2, linestyle=':', color='g')\n",
      "    p = fit.power_law.pdf()\n",
      "    #ax2.set_ylim(min(p), max(p))\n",
      "    ax2.set_xlim(ax1.get_xlim())\n",
      "    \n",
      "    fit = Fit(data, discrete=True)\n",
      "    fit.power_law.plot_pdf(ax=ax2, linestyle='--', color='g')\n",
      "    from pylab import setp\n",
      "    setp( ax2.get_xticklabels(), visible=False)\n",
      "    #ax2.set_xticks(ax2.get_xticks()[::2])\n",
      "    if ax2.get_ylim()[1] >1:\n",
      "        ax2.set_ylim(ax2.get_ylim()[0], 1)\n",
      "    \n",
      "    ax2.set_yticks(ax2.get_yticks()[::2])\n",
      "    #locs,labels = yticks()\n",
      "    #yticks(locs, map(lambda x: \"%.0f\" % x, log10(locs)))\n",
      "    if data_inst==1:\n",
      "       ax2.annotate(\"B\", annotate_coord, xycoords=\"axes fraction\", fontsize=14)        \n",
      "       ax2.set_ylabel(r\"$p(X)$\")# (10^n)\")\n",
      "        \n",
      "    ax3 = fig.add_subplot(n_graphs,n_data,n_data*2+data_inst)#, sharex=ax1)#, sharey=ax2)\n",
      "    fit.power_law.plot_pdf(ax=ax3, linestyle='--', color='g')\n",
      "    fit.exponential.plot_pdf(ax=ax3, linestyle='--', color='r')\n",
      "    fit.plot_pdf(ax=ax3, color='b', linewidth=2)\n",
      "    \n",
      "    #p = fit.power_law.pdf()\n",
      "    ax3.set_ylim(ax2.get_ylim())\n",
      "    ax3.set_yticks(ax3.get_yticks()[::2])\n",
      "    ax3.set_xlim(ax1.get_xlim())\n",
      "    \n",
      "    #locs,labels = yticks()\n",
      "    #yticks(locs, map(lambda x: \"%.0f\" % x, log10(locs)))\n",
      "    if data_inst==1:\n",
      "        ax3.annotate(\"C\", annotate_coord, xycoords=\"axes fraction\", fontsize=14)\n",
      "\n",
      "    #if ax2.get_xlim()!=ax3.get_xlim():\n",
      "    #    zoom_effect01(ax2, ax3, ax3.get_xlim()[0], ax3.get_xlim()[1])\n",
      "    ax3.set_xlabel(units)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Figure 1"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "n_data = 3\n",
      "n_graphs = 4\n",
      "f = figure(figsize=(8,11))\n",
      "\n",
      "data = words\n",
      "data_inst = 1\n",
      "units = 'Word Frequency'\n",
      "plot_basics(data, data_inst, f, units)\n",
      "\n",
      "data_inst = 2\n",
      "#data = city\n",
      "#units = 'City Population'\n",
      "data = worm\n",
      "units = 'Neuron Connections'\n",
      "plot_basics(data, data_inst, f, units)\n",
      "\n",
      "data = blackouts\n",
      "data_inst = 3\n",
      "units = 'Population Affected\\nby Blackouts'\n",
      "plot_basics(data, data_inst, f, units)\n",
      "\n",
      "f.subplots_adjust(left=None, bottom=None, right=None, top=None, wspace=.3, hspace=.2)\n",
      "f.savefig('FigWorkflow.eps', bbox_inches='tight')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Calculating best minimal value for power law fit\n",
        "Calculating best minimal value for power law fit"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Calculating best minimal value for power law fit"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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nlezfr3974cJKPf+8UvPmKXX5stuKdwlWNenc7LB06aoKDv1ri9Gq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LgAFy8Cg8eHQmGWgSVLgO7d89n9UZAHTX2wWrVqAID9+/dj/PjxetdtqAwdyl59fN4eMNLgQGBE\ntGgB7NiBERvfBwAobwzFrNNz5NWkR2SbQnzhwgW4u7sjKCgo1/HBgwfj8uXLsLGxQffu3dGsWTN4\nenpmnX/w4AGeP3+Oa9euISEhAQ0aNECFChX0LZ8rzM2BLUsbIMRmDMI3LMbZsyUxbRqwbJncyvhG\nUx8EgKNHj6J+/fqoWLGiPiUbNB99BJQuDVy/zlY2ONSPh20x49/ASWD4dOlmDgcH4MGDCth64DG+\ncApEiyot5Jalc2QL4T08PGD7zu5uERERAAAbG5ba0tHREX5+frnKTJgwAW5ubjAzM4OFhQVKly6t\nH8GcY2luiWPTZqLYZ4NgbqHE8uXA4cNyq+IbTX3w4MGDmD9/Pnbu3Ilp06bpR6wRYG0NfPIJe7/G\nOxaN1jTCm+Q38ooSCFTAzAz44gv23v72Ekw49CPw6BFw8qS8wnQMV4uQr1+/Djs7u6zPDg4OCAgI\nyFPO3t4eh9RYc5JzRqcxTlbMpHqp6vh9/Hj0D5+HuCOzMXw4G0KrWVNuZbojc3KiVKjig+7u7nB3\nd1f72qbih4UxdCiwYQNweE8puK3pidn+s7HSzfAzgErthwL++OILtmos+G97KM7vRfM6iegXFYJZ\nUwNgPmMam4FrbJCMnDlzhlxcXLI+R0REUNOmTbM+T5o0idavX69VHTL/RFnw8ptLXa2PE0Dk4kKU\nlCS3Iv2hrr314YOa6DJWlEqiOnWIAKJfNsZSuUntaP+pQLrZ4zu6GZRCN28S3bxJ9Pq13Eq1g0d7\nAyAvLy86c+aM3FIMFm9vog4diIoVYz4MEI2vtINo+HCitDS55RERa9O8vLwk8UGuZgnVqFEDAJD4\nNk97YGAgunTpovV1TW3t72zXmdjx0T7UqhCLa9eAUaOMf7m5VGt/deWDgOn5YX4oFNmTFcd8VRIv\nl55H/+7N0fjkCjRuXgyNG7Nl6MeOyatTU3jfi0GgHSNGsO3L37xh++NYWgIroj/DhquOLA+Nkc0O\nl22Z47lz5+Dj44MTJ05g1KhRmDBhAqytrREaGopt27ZBoVCgVatW6N+/v1b1mOzSnu3bEbQlAG0u\nLkdSErBmjVGnvs9CHXvrywczdRlrPg51efYMGDgQeP4cAAgPXj9ApXRrFE9KA+zYeNjSpSyLnaGh\nz3wc6mKybaEO2byZBQ0WFoSTrWej89gm2RNtZMZk8yCog8k2zM+eAQ0aYOfqFxg81Bw2NmxOjbEu\n+OC5YQZE41wYYS/CUJqKoVIDJyAoCHjbi2PI8Ghvk20LdcykyYSflypQtiwhOFghu/tK2RZyNcSg\nK+bMmWN6N0TlykD16viscSB69gSSkoB16+QWpTtcXV2579oVQwz5U698PVSqYA/07Mn2NDdgxBCD\n6aHoNh31W9/Hq1cKzJsntxppMYkeBCP/iQUzYQLQti2OlfwIvd2sULky2xXakHYkUxde7c2rLq7Y\nvZsN7O7eLbcSreHR3jxqMgbuvbwHlwWDEbv8IszMFAgLAxwc5FZl4JkU9YnJPrktWwYMGIC2HZNR\nrPpNPHsG7NzJTr15A7ydh2cUiCc3I6BfP2DXLrlVGDUm2xbqkDrl6mBinw9Rta0/0tMhey+CyW/W\npA4iambM++UhZo21R536KejW2QqbNwPNmwNXrhjX8l1e7S3Gf00DnufC8HpvGAMp6Slo9L8+eLjg\nOBQww+3bQB2zcMDLC/jtN1nSiotJiiogbgpGaipQuUYCXj/PvctjcDDQtKlMonQAr/bmVRdvZCgz\n4P6HOzb12YRKJSrJLUdjeLS3CFJ1i1+4H/p8+gIJVwZi2DDgt00ZQPv2wGefAWPH6k2HlEGqCBBM\niE2bCF+NzIB9m2toXKo1jh1TYMECtm20scCrvUXjrDqTTk5CTGIMfnP/TW4paiN6EEybLX5n8VWP\njiBS4NYtoJ7yNtCuHdtRr149vWoRPQgqIG6K3MSnJODHv/8Hlzfz8PEAS7RpA/zzj9yqpINXe/Oq\ni0fiUuLQeG1j7PLYhfY128stRyN4tDePmoyRoUOBbduARYuAqVPB9jffs4dlWDI315sOMUlRRUx6\nYk5KCvDnn1kfba1K4KduP6HnB5YoVgy4dAmIjpZRn0SISYrGQ8m4FGyuNhqjjo5CWkaa3HKMCpNu\nC/VEZuLVrC1cxo1jr1u26KV+MUlRDUw+ak5JAcqVY2nrihfPdcrNDThxgs2hGTZMHnlSw6u9xRCD\nGly4ABo9Gj0mVULPuj0xoc0EuRWpjBhiEISEAM2aAbVqAffvvz144wZrg3v00JsOMcSgAuKmANCy\nJevmatcu1+FffmFzZzw82PJzY4BXe/Oqi0syMoAqVXD/1G74Uzi+dPxSbkVqw6O9edRkjKSnA6VK\nseR0L16w57P8iI8HrKzYfg66QAwxCFTDxQW4di3P4Y8+Yq8nTpCx7TEiMGTMzYFevVD7wk2DDA4E\npo2FBVtCDgDfbvLOt8yjR0DVqmwfB54RAYIp0LIlcPVqnsP29kDTpoT4eAWmLbpv9Ds+CgyIjz4y\n+LTLPCLmIOgHFxf2etQ/CpceX8pz/vhx1oOwe7f0CevEHAQ1EN1qYINiAwYAt2/nObVsGTBxInvf\no2cKNm+0QvXqetYnIbzam1dd3BIbyzZtevIEKFlSbjVqo2t7b926FWfPnoW5uTmCgoJw5coV2TUJ\nsvntN+CLL4DWPR4iuV9fXPv6GizMLLLODxkCbN/O3h87xrYhkRoxxKAiJh81N2oEdO8OKJV5Tn3/\nPbBpE2BVIgknj1vB1ZWQkiKDRi0xhFUMJu+H6lCqFFsnlpQktxK10Jcfdu/eHZs3b8by5cvx6aef\n6rw+gXo4O7PX6LCaqFC8An658kv2yTdv8PepbL8+flzP4tRA9CAIAAAPI9LRqNUTJEXZY8UK4Lvv\n5FakGbzam1ddhoRPkA862XeCfRn7POfu3GEb5BQrpn9d+aGqvaOiojBz5kwEBwfn6gUICQnBzp07\nYWZmBicnJ3h4eMDb2xtBQUFYsmQJrN/uuLZu3Tq4u7ujSpUqkmkSaE/OiYqX7oSh94E2CPomCNVL\nVUfEPxGo2c4uq2y9esx/pUb0IAgkw97OAmtXsK7cuf9LR2wscOsW0KQJMHq0zOIEAgAPXz/E+BPj\n8xx//Rro2hVo1YqNphkSFy5cgLu7e56GfPDgwZg9ezbmz5+PdevWISwsDJ6enli9enVWcEBEePbs\nmUrBgUC/5JyoGPewHhZ2XYjXya8BABceseCgR4OHKFMGCAsD7t2TS2nhmESAILp2VWPYx+XQ8v0U\nvHppgdGjgY4dgX//ZUMQyclyqyscQxhiEGjH5HaTERodimNhx3Idf/qU9RwEBbHJYUuWsJWShoCH\nhwdsbW1zHYuIiAAA2NjYAAAcHR3h5+eX57vHjh1Dr169dC9SoBGZExUDAoCvnL/Ce5XeAwCcP8+O\nu0bvRvduLDA8cUIOhUVjUXQRw0f8x6EaCgWwbIkVOnQAduzIPp6aylZJtuc4621mAqK5c+fKLUWg\nI6wtrLG652p8e+xbdHboDBtL9h9o48YsOJg4EdiwAZgyhS2A2LqVJasxNK5fvw47u+wuaAcHBwRk\npeXLpnfv3mpfO2dbKJJ26ZbMeQjvrjDPDBDaV7iFyjX/xR40wfHj2vfUZibpkhKT6EEQqE779kDf\nvux9v37Al2+XoV+4IJ8mgSATt7puaFGlBX668FOu47a2wPr1wJEjQOXKwN9/s2x2mzbB4JbvOjs7\nZ/UiAEB4eDhcMh9HJcDV1RVz5swRwYGOyQwQcsZ2r1+zHXSLFQNafuOMD8LXAwD8/KD15HBd2NUk\nAgQxxPCWX35hy8aKYNcu4PRptka3c2d2LDPq5RVDGGIQfqghffsCDx5kfVzxwQpcfHwRSsq7Kqd3\nbyA0lK3qjY8HPD3Z1589049UKfywRo0aAIDEtwvkAwMD0SUzwb+WiMBAfzRqBNjYAOHhwMuX7NjF\niyxgdXEBrId/iurTh6JZM5YLQao2NjNQkAQyckzgJ6pO795E+/er9ZXTAXcJICpXjigjQ0e6JIRX\ne/OqyyAYNoxo1Sq1vqJUEm3bRlS6NBFAVKEC0cGDupGXH6ra++zZszRixAiqUaMGzZ8/n5KSkoiI\nKCQkhKZMmUJTp06lffv2SabJy8uLzpw5I8n1BEXTpg3zv1On2OcffmCfu3x+hZRKJRERTZnCjk2a\nJE2dZ86cIS8vL0naHJPoQRC8pVEj4L//1PpKaOoxWJaJxsuX+eZZEgh0jwZZFRUK4PPP2aqGrl2B\nmBggKkpH+rSgY8eO8Pb2RkREBH744YesFQpNmjTBTz/9hEWLFqF///4yqxRoSuYww8qVLPdXZi/B\n/ZI++D30dwBs0zyAz3wIIkAwJRo1YmsX1WBs6zGo1PAuAP6HGQRGSo8ebF/y2Fi1v2pnB5w8Cezf\nD3z9tQ60CQSFMGwY20T3yBGgRQvg8mV2/NdvhmLiyYl4k/wG7dqxZKFWVkBCgrx638UgEyXt3r0b\nRISYmBh8++23hZYVyUFycPEi25s8n30ZCmPxsmRMnWiNDn3u4f/t3XtcTVn/B/DPIVS6EI3LyL2i\nKIlQQ2XGQ2Z+aIxojJHLuEQN5TpmVDNmRo88eblkiIRkXB8UIrpR6aqSkDFFRJIi5ZRq/f4403l0\nOTmnzmVX3/fr5aVz2Xt991mXs87ea68VdXaAjIKTDq7mN1fjajYmTRIMKPjqK0VHIhYu5jcXY2oN\n7t0D7O0FKz4Dgrtubt8Gvgv6TnhnzuvXgomVpKlVTpSUkpKCixcvoqCgAJaWlmJtQ4PD/jFokOAM\ngoSF5lNLwWnP6GgeMvIzZBFZkzWHQYqkCf7v/4DIyHpfelH6Ao9ePZJzQM0TtYXyp68v+G22apXg\n0lf1FaPNn27GidsnkJSbBI2X2VK73aZFLNbU2ClGfX198fr1a2zYsAEzZ87EsWPHGkyHes21+PoC\nDg4SLUJeUQF06iQ4/bUn4iwWWU6VXXxNxNX85mpczUZ5uaDM8nh1XtoVvwun757GlTlXwKvndUXg\nYn5zMabW5tUrwZmC6mJ6MOUg8t48w5oFfsDhw4LpQKVEGvmtsImSqqcYTU1NrfH87NmzERcXBxUV\nFUyYMAFGRkZYuHCh8HV9fX3c+2e0XFlzXFVI0b77TuJNlJSA0aMFtz6e2zIVU/QBmt2VyFUDiyws\nHrEYvsm+OHb7GGYNoYWLGlJ9myPd6qgYmpo1H88dNlfwh81TwRkyKXQQpDlhksIuMTR2itFx48ah\nqKgIfn5+tIqZHP30k6Dne/68YH0Grk4NSlofpTZK8PncB66XXfG6TPKBjK0JzYPAUQYGEt9hJoo0\n50Hg1BgEcaYYVVZWxk8//YT58+dTB0GOLC0FE9BMmAAUFADffgu8e6foqAgRMNcxx8QBE+EW4abo\nUAiRnIEBkMG98V2cWotBVlOM0vzj0qGjIzhzYGAgGOsYEiIYO6ZIsph/nDRPnp95YujuoVhtvho9\n1XsqOhxOoksMHFU9Rw1j9Y6zkUSLuMRQH1lOMUrzj0sHjye4txcAtu15iW9Of6PQgU/NKV9pBLkU\nPH4MJCfX+5J2R23cWXZHoZ0Drt9N01zqSqvTpQtgbo6U+9dQXlnepF1J8xKDwu5iiIqKwqFDh3Dp\n0iUsXboULi4uUFZWRnp6Og4fPgwejwczM7MmzyJGI3frMXeuYF0GdfVGbf74MdC7N9CuHcOQf/8L\n9iMnYpX5KikH2ThczW+uxtXs/Pe/gI8PEBqq6EgaxMX85mJMpKZpf06D2cdm+GHsD03elzTyu1lO\nlCQJHo8HNzc3Oq32PkNDIDAQMDZu9C7+9S9BG/2LVwF2MAOcnHESY/uMRUqK4NLD4sVA585SjPkD\nqk+reXh4cLIRpHIoJW/eAD17Cnqp0p5ZRgq4XA6pg8B92UXZGLF3BBK+S0C/zk1bq5w6CGKgSlGP\nKVMEcyE04ezMkSOCue7NzICNh89jcfBiBH+Rgs/Mu6KgQNCG79sH2NhIL2xxcKfecQAAACAASURB\nVDW/uRpXs2RjI1iHfMYMRUciEhfzmzqpzcPv135HdE40guyDGjWvhzQ7qZwag0DkZMAA4MGDJu3C\n1lZwhSI+HuDf+hzfDHHAp1OfoqAA6NgRyM0FJk8WzI5L01UI0BgEKZFg8aayCvkWPhqDQJrK1dwV\nfxf+jTN3zzRq+xZ7m6OsUMNcy4ABwN9/N2kXqqr/W/zmq6+AkDW/4OXdoejeHbh/H9iyRbD4SF5e\ng3PcSA3XG2aAGmep+eILwdJ3lZUNvi0mJwbj/Mehsqrh90mTNBtn0jq1b9sePp/74OeonxV+Foou\nMbRGFy8C3t6CZe6aoKoK2L4dWL8e4PMFdziEhgqW1wUEd+106gT06CGFmMXE1fym07tStm2b4PRU\nrcnW3lfFqjDuwDh8Y/QNloxYIpewaAwCaZKQEFQv7/im/A3U2osu3x9CYxDEQJWiHoWFgiXGRo+W\nyu7u3QPc3QUdg/dmxVYIruY3V+Nq6dLy0vDZoc9w2/E2tDtqyy1dLuY3F2MitYweDXh5AZ980uRd\nUQdBDFQpWheu5jdX42oNXC65oIhfBL+pfnJLk4v5zcWYSC3z5gHm5o1aM6e2VrncM2k+bj69qegQ\nOIXGwiiGu5U7Lj24hOhH0TJPqzmMhSEcxrEpl1vFGQS69it/pe9KYehjiK3/2oovBzdtsitxcPna\nL0C/3hQt7nEcBmoNRBfVLnJJj4v5zcWYSC3BwYJJ7EJCajxdWVUJfgUfHdt3FHtXdIlBDFQpFCf+\nSTy+CPwCMQtiMFBroFzS5Gp+czUuIhtczG/6sdQMPHgAWFsDjx7VeNorxgt3XtzB/in7P7gLmgeB\nNAtmH5tho+VGzDgxA2/fvVV0OApHlxikrKxMMOL7A7c7yhNdYiBN0revYCKwqqoaTy8yXYRLf8nn\nMtn7qIPQWkVFAWvWyDyZZSOXQa+LHr4P+V7maXEdzYMgZR06AC9ecOqaLc2DQJqkbVtgzx6gTc2v\nZo0OGvjPxP9gyfkleFf5Tm7h0CWG1iomBnB1BWJjZZ5UcVkx7E/ZI+DLAHRS7iTTtLia31yNq9mb\nO1dwS5gURn1LExfzm4sxEfExxjDpyCRM6D9BrMXx6C4G0ni9e9e5ziUr6h3UEfx1sMw7B6QVGj0a\nuHFD0VE0G3SZq/ni8XjYNXkXNl/fjCevn4h8nzQvc1EHobXq0UNwera8aWuPE/FR4ywDo0YBcXGK\njkKIxiAQWRqoNRCXvrmEHurymZ62VVxioJG7IvTpA0REAP2atqwoF9Btjq3Uu3eCdcWfPAE0NRUd\njRAX85uLMRHZodscxUCVogFjxwKbNgGWloqORGq4mt9cjatFeP4c0NYWLAbCEVzMby7GRETYsgVw\ndhYMxG0kGoMgJjq1K8KBA4CpqUKSXndlHRKeJEhtf3RqtxX76CNOdQ64jNrCZmL/fsGyuI0gzbaQ\nziAQhTiVcQqrQlchaVEStFS0pLZfruY3V+MissHF/OZiTESEL78EZs0C7OwavQs6g0CarekG0zFt\n0DRsvr5Z0aEQ0mrQGYRmYvBg4M6dD74t/Xk6ph+fXqMjQGcQJECDFLmrvLIcjDF0UGr8dbZqzWGQ\nIpXDlo/L5ZDOIDQjAQFAUBBw7FiDb6uoqsBI35FwHeOKb4y+qfEaDVIUA1WK1oWr+c3VuFqMigqg\ntBTQ0FB0JAC4md9cjImIkJwMODgAaWkffGvc4zhMOzYNGY4Z6KzSWfg8XWIghBAA2L4d2LBB0VEQ\nIh2DBgGLF4v11lG9RmHaoGnYECb98k8dhNbO1BQoKlJ0FM2StbU1oqPlu3gKEcHMjGZUFAONQWgm\nVFWBZcvEfvtv43/Df+/+F0m5Sa17DML9+/exfft2jBgxApmZmfj1118bfD+dVvuAIUOAwEDAyEjR\nkUiFvPL78uXL2LFjB9avXw9zc3POxNVqlZYCXbsCBQWAioqio5F5fufk5MDX1xeGhobQ0NCAjY2N\nwmMiipWWlwb9LvrCMV2t8hJDz549UVpaivT0dJiYmIi1DfWaG6CjA+TkKDqKJpP3PAhJSUkYMWIE\nNbhcoaoKGBgIrt22AmFhYRg2bBhmzpyJvXv3KjocwgFG3YykMuD7fQrrIDx79gwLFy6EmZlZjedv\n3bqF9evXY8OGDTh16hQAYN++fXBycgKfz0doaCgsLCywZcsWHDp0SKy0ZL3Mrjw6HzJL4+OPgdxc\n2abxHlml0ZhldhtbBk+fPg1bW1tphd6iybVjPno0p9ZlEEdjy+CMGTPw4sUL+Pv7I/ef+stlivyB\n1lrTlgYlRSUcHR2NadOmITU1tcbzs2fPRlxcHFRUVDBhwgQYGRlh4cKFwtdfv36Nzp0FIzV5HJk9\nLSIiQua3rsksjR49anQQmu1xNEJjy2B2djby8/ORmJiIkpIS6Ovro2vXrvIOv1mQa35bWQHp6fJJ\nS0qa0g7a29tDTU0NkZGR8g5bYoqs9601bWlQ2BmE6dOnQ01NrcZzOf+c6lb55xqiiYkJwsLCarxn\nypQpSExMxJ49e/DVV181OY7aPbz3H9f3d/V9zrX/bg5p1Pd/xJs3QG7uB9Oo73Wx06j1nKzSkLS3\n3tgy6OLigkmTJqFNmzZQUlKCphwXCZLkGBvzeYt6vqHyVfuxLH41ibXPr74CxLicyKXjbmwZzMrK\ngouLC3bv3g1nZ2eJ0xVF3M9G0rpPaTci7StXgPnzgX8uY8oi7Q/h1BiE5ORk6OjoCB/37dsXSUlJ\nNd7TqVMn/Prrr1i8eDHmzJnT5DTFrfCivvDEyQyupFFvYVJRATw9G9WoSlpgZZ2GNCqGOGUQAPr0\n6YOzZ8/it99+Q7t27Zqcrrik0fB86PUP5cOHHkuzgWrMPpv7cYtTBo2NjeHr6wtHR0exx2KJQ9zP\nRhZfVpR2reevXwcuXhSsVCqjtD+IKVB4eDgbMWKE8HFOTg4bOnSo8PGqVavYnj17mpQGAPrXyv5x\nrQxSOWyd/6gM0j9F/2sqhY1BqE+vXr0AAKWlpVBVVUVKSgoWizlZhCiMRpkTCciiDAJUDon4qAwS\nrmjrrqA1cqOionD48GGkpqaCz+dj5MiRUFJSwtixY7F9+3ZcvXoV06ZNg4WFhSLCI60AlUGiaFQG\nCZc1u4mSCCGEECJ7nBqkSAghhBBuoA4CIYQQQuqgDgIhhBBC6qAOAiGEEELqoA4CIYQQQuqgDgIh\nhBBC6uDUREnyUlZWBm9vb2hqakJPTw+ffvqp1NOorKzE5s2b8ejRI+zZs0fq+w8KCsLdu3fBGIOp\nqalMjiEtLQ0JCQng8/ng8/lwdXWVehrVrK2tsWnTJpnc752dnQ0nJyd0794d48ePh729vdTTkJQ8\nyiAXybpecJU86quk5Fm/RZFlvRdF0e3B8ePHwRjDixcvsGzZMrmle/DgQURGRqJt27ZITU1FfHz8\nB7dplWcQYmJi0K1bNyxdulTsJaMlVVJSAhsbG1RVVclk/6ampli9ejW+++47mR2DkZERrK2tERcX\nJ9MVyS5fvgw1NTWZrc7J4/FgYGAAc3NzjBo1SiZpSEoeZZCLZF0vuEoe9VVS8qrfosi63ouiyPYg\nJSUFFy9eREFBASwtLeWa9oQJE+Dn5wdvb2/MmjVLrG1azBmEZ8+e4ccff0RaWlqNntGtW7cQGBiI\nNm3aYPjw4Zg+fTrS0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0aNwr1796Cvr4+UlBRMnjxZuL/a5UWU6i/z0aNHw87ODv369cPL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\nIYTUQR0EQgghhNRBHQRCCCGE1PH/vfdFJSSYxhMAAAAASUVORK5CYII=\n"
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "blackouts = blackouts/10**3"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 95
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Introduction"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = blackouts\n",
      "####\n",
      "import powerlaw\n",
      "fit = powerlaw.Fit(data)\n",
      "fit.power_law.alpha\n",
      "fit.power_law.sigma\n",
      "fit.distribution_compare('power_law', 'exponential')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Calculating best minimal value for power law fit\n"
       ]
      },
      {
       "output_type": "pyout",
       "prompt_number": 8,
       "text": [
        "(12.754562675882063, 0.1522925560442657)"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Basic Methods"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Visualization"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### PDF Linear vs Logarithmic Bins"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = words\n",
      "####\n",
      "figPDF = powerlaw.plot_pdf(data, color='b')\n",
      "powerlaw.plot_pdf(data, linear_bins=True, color='r', ax=figPDF)\n",
      "####\n",
      "figPDF.set_ylabel(r\"$p(X)$\")\n",
      "figPDF.set_xlabel(r\"Word Frequency\")\n",
      "savefig('FigPDF.eps', bbox_inches='tight')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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NAwbAY49BvXpWRyZiHyWYMlCCESsYhrm22XvvmVNrvv66ZJ1NEXegBFMGSjBi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\nRK5CYII=\n"
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Figure 2"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = words\n",
      "fit = powerlaw.Fit(data, discrete=True)\n",
      "####\n",
      "figCCDF = fit.plot_pdf(color='b', linewidth=2)\n",
      "fit.power_law.plot_pdf(color='b', linestyle='--', ax=figCCDF)\n",
      "fit.plot_ccdf(color='r', linewidth=2, ax=figCCDF)\n",
      "fit.power_law.plot_ccdf(color='r', linestyle='--', ax=figCCDF)\n",
      "####\n",
      "figCCDF.set_ylabel(r\"$p(X)$,  $p(X\\geq x)$\")\n",
      "figCCDF.set_xlabel(r\"Word Frequency\")\n",
      "savefig('FigCCDF.eps', bbox_inches='tight')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Calculating best minimal value for power law fit\n"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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VKoSEhNC3b1/uu+8+fvvtN/bs2UPv3r2tEoQtaQtG2VpGhlSB37jxfBX4666D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\n"
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = blackouts\n",
      "fit = powerlaw.Fit(data)\n",
      "###\n",
      "x, y = fit.cdf()\n",
      "bin_edges, probability = fit.pdf()\n",
      "y = fit.lognormal.cdf(data=[300,350])\n",
      "y = fit.lognormal.pdf()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Calculating best minimal value for power law fit\n"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Identifying the Scaling Range"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = blackouts\n",
      "####\n",
      "import powerlaw\n",
      "fit = powerlaw.Fit(data)\n",
      "fit.xmin\n",
      "fit.fixed_xmin\n",
      "fit.alpha\n",
      "fit.D\n",
      "fit = powerlaw.Fit(data, xmin=1.0)\n",
      "fit.xmin\n",
      "fit.fixed_xmin\n",
      "fit.alpha\n",
      "fit.D"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Calculating best minimal value for power law fit\n"
       ]
      },
      {
       "output_type": "pyout",
       "prompt_number": 12,
       "text": [
        "0.37601504850371759"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = blackouts\n",
      "####\n",
      "fit = powerlaw.Fit(data, xmin=(250.0, 300.0))\n",
      "fit.fixed_xmin\n",
      "fit.given_xmin\n",
      "fit.xmin"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Calculating best minimal value for power law fit\n"
       ]
      },
      {
       "output_type": "pyout",
       "prompt_number": 13,
       "text": [
        "272.0"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = blackouts\n",
      "fit = powerlaw.Fit(data)\n",
      "####\n",
      "fit = powerlaw.Fit(data, xmax=10000.0)\n",
      "fit.xmax\n",
      "fit.fixed_xmax"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Calculating best minimal value for power law fit\n",
        "Calculating best minimal value for power law fit"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      },
      {
       "output_type": "pyout",
       "prompt_number": 14,
       "text": [
        "True"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Figure 3"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = words\n",
      "#FigCCDFmax = powerlaw.plot_ccdf(data, linewidth=3)\n",
      "fit = powerlaw.Fit(data, discrete=True, xmax=None)\n",
      "FigCCDFmax = fit.plot_ccdf(color='b', label=r\"Empirical, no $x_{max}$\")\n",
      "fit.power_law.plot_ccdf(color='b', linestyle='--', ax=FigCCDFmax, label=r\"Fit, no $x_{max}$\")\n",
      "fit = powerlaw.Fit(data, discrete=True, xmax=1000)\n",
      "fit.plot_ccdf(color='r', label=r\"Empirical, $x_{max}=1000$\")\n",
      "fit.power_law.plot_ccdf(color='r', linestyle='--', ax=FigCCDFmax, label=r\"Fit, $x_{max}=1000$\")\n",
      "#x, y = powerlaw.ccdf(data, xmax=max(data))\n",
      "#fig1.plot(x,y)\n",
      "####\n",
      "FigCCDFmax.set_ylabel(r\"$p(X\\geq x)$\")\n",
      "FigCCDFmax.set_xlabel(r\"Word Frequency\")\n",
      "handles, labels = FigCCDFmax.get_legend_handles_labels()\n",
      "leg = FigCCDFmax.legend(handles, labels, loc=3)\n",
      "leg.draw_frame(False)\n",
      "savefig('FigCCDFmax.eps', bbox_inches='tight')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Calculating best minimal value for power law fit\n",
        "Calculating best minimal value for power law fit"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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16KCutRkers789/ODtDSzhSAsmWIkKSkpxirK6Iz4Ms0uJiZG0el0Srt27RQ/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\nAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x2eea950>"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Continuous vs. Discrete Data"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = blackouts\n",
      "fit = powerlaw.Fit(data)\n",
      "####\n",
      "fit = powerlaw.Fit(data, xmin=230.0)\n",
      "fit.discrete\n",
      "fit = powerlaw.Fit(data, xmin=230.0, discrete=True)\n",
      "fit.discrete "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Calculating best minimal value for power law fit\n"
       ]
      },
      {
       "output_type": "pyout",
       "prompt_number": 16,
       "text": [
        "True"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Comparing Candidate Distributions"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = blackouts\n",
      "fit = powerlaw.Fit(data)\n",
      "####\n",
      "fit.power_law\n",
      "fit.power_law.alpha\n",
      "fit.power_law.parameter1\n",
      "fit.power_law.parameter1_name\n",
      "fit.lognormal.mu\n",
      "fit.lognormal.parameter1_name\n",
      "fit.lognormal.parameter2_name\n",
      "fit.lognormal.parameter3_name == None"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Calculating best minimal value for power law fit\n"
       ]
      },
      {
       "output_type": "pyout",
       "prompt_number": 17,
       "text": [
        "True"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = blackouts\n",
      "####\n",
      "fit = powerlaw.Fit(data)\n",
      "R, p = fit.distribution_compare('power_law', 'exponential', normalized_ratio=True)\n",
      "print R, p"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Calculating best minimal value for power law fit\n",
        "1.43148048496"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 0.152292556044\n"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Generative Mechanisms"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = worm\n",
      "fit = powerlaw.Fit(data, discrete=True)\n",
      "####\n",
      "fit.distribution_compare('power_law', 'exponential')\n",
      "fit.distribution_compare('power_law', 'truncated_power_law')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Calculating best minimal value for power law fit\n",
        "Assuming nested distributions"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      },
      {
       "output_type": "pyout",
       "prompt_number": 5,
       "text": [
        "(-0.081336372762826459, 0.68670761175575712)"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = worm\n",
      "fit = powerlaw.Fit(data, discrete=True)\n",
      "####\n",
      "fit.distribution_compare('power_law', 'exponential')\n",
      "fit.distribution_compare('power_law', 'truncated_power_law')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Calculating best minimal value for power law fit\n",
        "Assuming nested distributions\n"
       ]
      },
      {
       "output_type": "pyout",
       "prompt_number": 57,
       "text": [
        "(-422.43094963299131, 0.0)"
       ]
      }
     ],
     "prompt_number": 57
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = words\n",
      "fit = powerlaw.Fit(data, discrete=True)\n",
      "####\n",
      "print fit.distribution_compare('power_law', 'exponential', normalized_ratio=True)\n",
      "print fit.distribution_compare('power_law', 'truncated_power_law')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Calculating best minimal value for power law fit\n",
        "(9.1359147187770002, 6.4856142413795328e-20)"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Assuming nested distributions\n",
        "(-0.91712308337346782, 0.17562683168707593)"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print fit.distribution_compare('power_law', 'truncated_power_law')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Assuming nested distributions\n",
        "(-13026.994760437048, 0.0)"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      }
     ],
     "prompt_number": 68
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Figure 4"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = words\n",
      "fit = powerlaw.Fit(data, discrete=True)\n",
      "####\n",
      "fit.distribution_compare('power_law', 'lognormal')\n",
      "fig = fit.plot_ccdf(linewidth=3, label='Empirical Data')\n",
      "fit.power_law.plot_ccdf(ax=fig, color='r', linestyle='--', label='Power law fit')\n",
      "fit.lognormal.plot_ccdf(ax=fig, color='g', linestyle='--', label='Lognormal fit')\n",
      "####\n",
      "fig.set_ylabel(r\"$p(X\\geq x)$\")\n",
      "fig.set_xlabel(r\"Word Frequency\")\n",
      "handles, labels = fig.get_legend_handles_labels()\n",
      "fig.legend(handles, labels, loc=3)\n",
      "savefig('FigLognormal.eps', bbox_inches='tight')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Calculating best minimal value for power law fit\n"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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ZQq9ekP9BbQiaxpkzULs2hIc/tdPVq4bG/5kzZej/bEISjBDC5PLkgS++SFw+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\nYII=\n"
      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Creating Simulated Data"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "empirical_data = blackouts\n",
      "####\n",
      "fit = powerlaw.Fit(empirical_data)\n",
      "simulated_data = fit.power_law.generate_random(10000)\n",
      "\n",
      "theoretical_distribution = powerlaw.Power_Law(xmin=5.0, parameters=[2.5])\n",
      "simulated_data = theoretical_distribution.generate_random(10000)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Calculating best minimal value for power law fit\n"
       ]
      }
     ],
     "prompt_number": 127
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "theoretical_distribution = powerlaw.Power_Law(xmin=5.0, parameters=[2.5])\n",
      "simulated_data = theoretical_distribution.generate_random(10000)\n",
      "####\n",
      "fit = powerlaw.Fit(simulated_data)\n",
      "fit.power_law.xmin, fit.power_law.alpha"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Calculating best minimal value for power law fit\n"
       ]
      },
      {
       "output_type": "pyout",
       "prompt_number": 42,
       "text": [
        "(5.5253208595576631, 2.5298369451264975)"
       ]
      }
     ],
     "prompt_number": 42
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "powerlaw.plot_pdf(simulated_data,linewidth=3)\n",
      "fit.power_law.plot_pdf(simulated_data,linestyle='--',color='r')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 47,
       "text": [
        "<matplotlib.axes.AxesSubplot at 0xd829dd0>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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S4sxLicgJHTrANdec2Z6ScvbED3DJJcYWwCc9/3wjJw0YAPHxxkygLVtaGqqY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\nAAAASUVORK5CYII=\n"
      }
     ],
     "prompt_number": 47
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#Advanced Considerations"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Discrete Distribution Calculation and Estimation"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = blackouts\n",
      "####\n",
      "fit = powerlaw.Fit(data, discrete=True, estimate_discrete=True)\n",
      "fit.power_law.alpha\n",
      "fit.power_law.estimate_discrete\n",
      "fit = powerlaw.Fit(data, discrete=True, estimate_discrete=False)\n",
      "fit.power_law.alpha\n",
      "fit.power_law.estimate_discrete"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Calculating best minimal value for power law fit\n",
        "Calculating best minimal value for power law fit"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      },
      {
       "output_type": "pyout",
       "prompt_number": 22,
       "text": [
        "2.2691417084814285"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = blackouts\n",
      "####\n",
      "fit = powerlaw.Fit(data, discrete=True, xmin=230.0, xmax=9000, discrete_approximation='xmax')\n",
      "fit.lognormal.mu\n",
      "fit = powerlaw.Fit(data, discrete_approximation=100000, xmin=230.0, discrete=True)\n",
      "fit.lognormal.mu\n",
      "fit = powerlaw.Fit(data, discrete_approximation='round', xmin=230.0, discrete=True)\n",
      "fit.lognormal.mu"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 23,
       "text": [
        "0.39905257607693184"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "theoretical_distribution = powerlaw.Power_Law(xmin=5.0, parameters=[2.5], discrete=True)\n",
      "simulated_data = theoretical_distribution.generate_random(10000, estimate_discrete=True)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 125
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "empirical_data = blackouts\n",
      "####\n",
      "theoretical_distributionibution = powerlaw.Power_Law(xmin=5.0, parameters=[2.5], discrete=True, estimate_discrete=False)\n",
      "simulated_data = theoretical_distribution.generate_random(10000)\n",
      "\n",
      "fit = powerlaw.Fit(empirical_data, discrete=True, estimate_discrete=True)\n",
      "simulated_data = fit.power_law.generate_random(10000)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Calculating best minimal value for power law fit\n"
       ]
      }
     ],
     "prompt_number": 126
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Nested Distributions"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = blackouts\n",
      "fit = powerlaw.Fit(data)\n",
      "####\n",
      "fit.distribution_compare('power_law', 'truncated_power_law')\n",
      "fit.distribution_compare('exponential', 'stretched_exponential')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Calculating best minimal value for power law fit\n",
        "Assuming nested distributions"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Assuming nested distributions"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 7,
       "text": [
        "(-13.018342321459194, 3.3499122220614908e-07)"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Restricted Parameter Range"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = blackouts\n",
      "####\n",
      "fit = powerlaw.Fit(data)\n",
      "fit.power_law.alpha, fit.power_law.sigma, fit.xmin\n",
      "\n",
      "fit = powerlaw.Fit(data, sigma_threshold=.1)\n",
      "fit.power_law.alpha, fit.power_law.sigma, fit.xmin"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Calculating best minimal value for power law fit\n",
        "Calculating best minimal value for power law fit"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Calculating best minimal value for power law fit"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Calculating best minimal value for power law fit"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      },
      {
       "output_type": "pyout",
       "prompt_number": 24,
       "text": [
        "(1.8833765811180314, 0.094168259953067143, 124.0)"
       ]
      }
     ],
     "prompt_number": 24
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "parameter_range = {'alpha': [2.3, None], 'sigma': [None, .2]}\n",
      "fit = powerlaw.Fit(data, parameter_range=parameter_range)\n",
      "fit.power_law.alpha, fit.power_law.sigma, fit.xmin"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Calculating best minimal value for power law fit\n"
       ]
      },
      {
       "output_type": "pyout",
       "prompt_number": 123,
       "text": [
        "(2.3000107113942141, 0.17069976919260452, 234.0)"
       ]
      }
     ],
     "prompt_number": 123
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "parameter_range = lambda(self): self.sigma/self.alpha < .05\n",
      "fit = powerlaw.Fit(data, parameter_range=parameter_range)\n",
      "fit.power_law.alpha, fit.power_law.sigma, fit.xmin"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Calculating best minimal value for power law fit\n"
       ]
      },
      {
       "output_type": "pyout",
       "prompt_number": 124,
       "text": [
        "(1.8833765811180314, 0.094168259953067143, 124.0)"
       ]
      }
     ],
     "prompt_number": 124
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Multiple Possible Fits"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Figure 5"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = blackouts\n",
      "fit = powerlaw.Fit(data, sigma_threshold=.1)\n",
      "print fit.xmin, fit.D, fit.alpha\n",
      "fit = powerlaw.Fit(data)\n",
      "print fit.xmin, fit.D, fit.alpha\n",
      "####\n",
      "from matplotlib.pylab import plot\n",
      "plot(fit.xmins, fit.Ds, label=r'$D$')\n",
      "plot(fit.xmins, fit.sigmas, label=r'$\\sigma$', linestyle='--')\n",
      "plot(fit.xmins, fit.sigmas/fit.alphas, label=r'$\\sigma /\\alpha$', linestyle='--')\n",
      "####\n",
      "ylim(0, .4)\n",
      "legend(loc=4)\n",
      "xlabel(r'$x_{min}$')\n",
      "ylabel(r'$D,\\sigma,\\alpha$')\n",
      "savefig('FigD.eps', bbox_inches='tight')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Calculating best minimal value for power law fit\n",
        "50.0"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 0.0998297854528 1.78313986533\n",
        "Calculating best minimal value for power law fit\n",
        "230.0"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 0.0606737962944 2.27263721983\n"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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js1IwbdvCl1/qcipxcTqB2kJKiu4KW79eJ5hHH9XDRmU1bpyOLSFB1/CsjMOH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\nbEFYbtaRG/gAAAAASUVORK5CYII=\n"
      }
     ],
     "prompt_number": 25
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## No Possible Fits"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = blackouts\n",
      "####\n",
      "fit = powerlaw.Fit(data, sigma_threshold=.001)\n",
      "fit.power_law.alpha, fit.power_law.sigma, fit.xmin, fit.noise_flag"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Calculating best minimal value for power law fit\n",
        "No valid fits found."
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "No valid fits found."
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      },
      {
       "output_type": "pyout",
       "prompt_number": 26,
       "text": [
        "(10.500000000422041, 5.1423189016918585, False)"
       ]
      }
     ],
     "prompt_number": 26
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fit.lognormal.mu, fit.lognormal.sigma\n",
      "range_dict = {'mu': [10.5, None]}\n",
      "fit.lognormal.parameter_range(range_dict)\n",
      "fit.lognormal.mu, fit.lognormal.sigma, fit.lognormal.noise_flag\n",
      "\n",
      "initial_parameters = (12, .7)\n",
      "fit.lognormal.parameter_range(range_dict, initial_parameters)\n",
      "fit.lognormal.mu, fit.lognormal.sigma, fit.lognormal.noise_flag"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Supporting Information"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from numpy import logspace\n",
      "from scipy.stats import variation\n",
      "import pandas as pd\n",
      "\n",
      "def validate(xmin, alpha, discrete='continuous', n_data=10000, n_trials=1):\n",
      "    \n",
      "    if n_trials>1:\n",
      "        return array([validate(xmin, alpha, discrete=discrete, n_data=n_data, n_trials=1) for trial in arange(n_trials)]).T\n",
      "        \n",
      "    if discrete=='continuous':\n",
      "        discrete = False\n",
      "        estimate_discrete = False\n",
      "    elif discrete == 'discrete':\n",
      "        discrete = True\n",
      "        estimate_discrete = False\n",
      "    elif discrete == 'discrete_estimate':\n",
      "        discrete = True\n",
      "        estimate_discrete = True\n",
      "\n",
      "    theoretical_distribution = powerlaw.Power_Law(xmin=xmin, parameters=[alpha], discrete=discrete)\n",
      "    simulated_data = theoretical_distribution.generate_random(n_data, estimate_discrete=estimate_discrete)\n",
      "    fit = powerlaw.Fit(simulated_data, discrete=discrete, estimate_discrete=estimate_discrete)\n",
      "    return fit.xmin, fit.alpha"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 38
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%prun\n",
      "xmin=1\n",
      "alpha=1.5\n",
      "n_data=10000\n",
      "discrete='continuous'\n",
      "validate(xmin, alpha, discrete=discrete, n_data=n_data, n_trials=10)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Calculating best minimal value for power law fit\n",
        "Calculating best minimal value for power law fit"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Calculating best minimal value for power law fit"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Calculating best minimal value for power law fit"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Calculating best minimal value for power law fit"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Calculating best minimal value for power law fit"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Calculating best minimal value for power law fit"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Calculating best minimal value for power law fit"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Calculating best minimal value for power law fit"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Calculating best minimal value for power law fit"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      }
     ],
     "prompt_number": 180
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "theoretical_xmins = unique(floor(logspace(0.0,2.0,num=20)))\n",
      "theoretical_alphas = array([1.5,2.0,2.5,3.0,3.5])\n",
      "#theoretical_xmins = [2]\n",
      "#theoretical_alphas = [2.5]\n",
      "distribution_types = ['continuous','discrete']\n",
      "n_trials = 10\n",
      "n_data = 10000\n",
      "\n",
      "ind = [(d,a,x) for d in distribution_types for a in theoretical_alphas for x in theoretical_xmins]\n",
      "ind = pd.MultiIndex.from_tuples(ind, names=['type', 'alpha','xmin'])\n",
      "df = pd.DataFrame(columns=['alpha_mean', 'alpha_sd', 'xmin_mean', 'xmin_sd'], index=ind)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 39
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "i = 0\n",
      "for dt, alpha, xmin in ind:\n",
      "    i += 1\n",
      "    print(i)\n",
      "    data = validate(xmin, alpha, discrete=dt, n_data=n_data, n_trials=n_trials)\n",
      "    df.ix[dt,alpha,xmin] = (mean(data[1]), std(data[1]), mean(data[0]), std(data[0]))\n",
      "\n",
      "filename = 'powerlaw_validation_%itrials_%idata.h5'%(int(n_trials),int(n_data))\n",
      "df.to_hdf(filename,'df')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1\n",
        "Calculating best minimal value for power law fit\n",
        "Calculating best minimal value for power law fit"
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        "\n",
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        "\n",
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        "Calculating best minimal value for power law fit"
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       "text": [
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        "Calculating best minimal value for power law fit\n",
        "Calculating best minimal value for power law fit"
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        "Calculating best minimal value for power law fit"
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        "Calculating best minimal value for power law fit"
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        "Calculating best minimal value for power law fit"
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        "6"
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        "\n",
        "Calculating best minimal value for power law fit\n",
        "Calculating best minimal value for power law fit"
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        "7"
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        "Calculating best minimal value for power law fit\n",
        "Calculating best minimal value for power law fit"
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        "Calculating best minimal value for power law fit"
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        "Calculating best minimal value for power law fit"
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        "Calculating best minimal value for power law fit"
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        "Calculating best minimal value for power law fit"
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        "Calculating best minimal value for power law fit"
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        "Calculating best minimal value for power law fit"
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        "Calculating best minimal value for power law fit"
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        "8"
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        "\n",
        "Calculating best minimal value for power law fit\n",
        "Calculating best minimal value for power law fit"
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        "Calculating best minimal value for power law fit"
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        "Calculating best minimal value for power law fit"
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        "Calculating best minimal value for power law fit"
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        "Calculating best minimal value for power law fit"
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        "Calculating best minimal value for power law fit"
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        "Calculating best minimal value for power law fit"
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        "Calculating best minimal value for power law fit"
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        "Calculating best minimal value for power law fit"
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        "9"
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        "\n",
        "Calculating best minimal value for power law fit\n",
        "Calculating best minimal value for power law fit"
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       "text": [
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        "10"
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      {
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       "text": [
        "\n",
        "Calculating best minimal value for power law fit\n",
        "Calculating best minimal value for power law fit"
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        "11"
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        "Calculating best minimal value for power law fit\n",
        "Calculating best minimal value for power law fit"
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        "\n",
        "Calculating best minimal value for power law fit"
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      {
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        "\n",
        "Calculating best minimal value for power law fit"
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       "text": [
        "\n",
        "12"
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        "\n",
        "Calculating best minimal value for power law fit\n",
        "Calculating best minimal value for power law fit"
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       "text": [
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        "Calculating best minimal value for power law fit"
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        "Calculating best minimal value for power law fit"
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        "\n",
        "Calculating best minimal value for power law fit"
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        "\n",
        "Calculating best minimal value for power law fit"
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        "Calculating best minimal value for power law fit"
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       "text": [
        "\n",
        "13"
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      {
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       "text": [
        "\n",
        "Calculating best minimal value for power law fit\n",
        "Calculating best minimal value for power law fit"
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        "\n",
        "Calculating best minimal value for power law fit"
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        "Calculating best minimal value for power law fit"
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        "Calculating best minimal value for power law fit"
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        "\n",
        "Calculating best minimal value for power law fit"
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        "\n",
        "14"
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        "Calculating best minimal value for power law fit\n",
        "Calculating best minimal value for power law fit"
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        "15"
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        "Calculating best minimal value for power law fit\n",
        "Calculating best minimal value for power law fit"
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        "16"
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        "Calculating best minimal value for power law fit\n",
        "Calculating best minimal value for power law fit"
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        "17"
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        "Calculating best minimal value for power law fit\n",
        "Calculating best minimal value for power law fit"
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        "\n",
        "18"
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        "Calculating best minimal value for power law fit\n",
        "Calculating best minimal value for power law fit"
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        "\n",
        "19"
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        "Calculating best minimal value for power law fit\n",
        "Calculating best minimal value for power law fit"
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        "Calculating best minimal value for power law fit"
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       "text": [
        "\n",
        "20"
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        "\n",
        "Calculating best minimal value for power law fit\n",
        "Calculating best minimal value for power law fit"
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        "Calculating best minimal value for power law fit"
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        "Calculating best minimal value for power law fit"
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        "Calculating best minimal value for power law fit"
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        "\n",
        "21"
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        "\n",
        "Calculating best minimal value for power law fit\n",
        "Calculating best minimal value for power law fit"
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        "Calculating best minimal value for power law fit"
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        "\n",
        "Calculating best minimal value for power law fit"
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        "Calculating best minimal value for power law fit"
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        "\n",
        "22"
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        "\n",
        "Calculating best minimal value for power law fit\n",
        "Calculating best minimal value for power law fit"
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        "Calculating best minimal value for power law fit"
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        "\n",
        "23"
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        "\n",
        "Calculating best minimal value for power law fit\n",
        "Calculating best minimal value for power law fit"
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        "Calculating best minimal value for power law fit"
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        "\n",
        "24"
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        "\n",
        "Calculating best minimal value for power law fit\n",
        "Calculating best minimal value for power law fit"
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        "Calculating best minimal value for power law fit"
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        "Calculating best minimal value for power law fit"
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        "\n",
        "25"
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        "\n",
        "Calculating best minimal value for power law fit\n",
        "Calculating best minimal value for power law fit"
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        "\n",
        "26"
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        "\n",
        "Calculating best minimal value for power law fit\n",
        "Calculating best minimal value for power law fit"
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        "\n",
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        "\n",
        "Calculating best minimal value for power law fit"
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        "Calculating best minimal value for power law fit"
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        "Calculating best minimal value for power law fit"
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       "text": [
        "\n",
        "27"
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       "text": [
        "\n",
        "Calculating best minimal value for power law fit\n",
        "Calculating best minimal value for power law fit"
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        "\n",
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       "text": [
        "\n",
        "28"
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        "\n",
        "Calculating best minimal value for power law fit\n",
        "Calculating best minimal value for power law fit"
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       "text": [
        "\n",
        "29"
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        "Calculating best minimal value for power law fit\n",
        "Calculating best minimal value for power law fit"
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       "text": [
        "\n",
        "30"
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        "Calculating best minimal value for power law fit\n",
        "Calculating best minimal value for power law fit"
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       "text": [
        "\n",
        "31"
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        "Calculating best minimal value for power law fit\n",
        "Calculating best minimal value for power law fit"
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        "\n",
        "32"
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        "Calculating best minimal value for power law fit\n",
        "Calculating best minimal value for power law fit"
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        "\n",
        "33"
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        "Calculating best minimal value for power law fit"
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       "text": [
        "\n",
        "34"
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        "Calculating best minimal value for power law fit\n",
        "Calculating best minimal value for power law fit"
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        "Calculating best minimal value for power law fit"
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       "text": [
        "\n",
        "35"
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        "\n",
        "Calculating best minimal value for power law fit\n",
        "Calculating best minimal value for power law fit"
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        "Calculating best minimal value for power law fit"
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       "text": [
        "\n",
        "36"
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        "\n",
        "Calculating best minimal value for power law fit\n",
        "Calculating best minimal value for power law fit"
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        "\n",
        "37"
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        "Calculating best minimal value for power law fit\n",
        "Calculating best minimal value for power law fit"
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        "\n",
        "38"
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        "\n",
        "Calculating best minimal value for power law fit\n",
        "Calculating best minimal value for power law fit"
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        "\n",
        "39"
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        "\n",
        "Calculating best minimal value for power law fit\n",
        "Calculating best minimal value for power law fit"
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       "text": [
        "\n",
        "40"
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        "\n",
        "Calculating best minimal value for power law fit\n",
        "Calculating best minimal value for power law fit"
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       "text": [
        "\n",
        "41"
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        "42"
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        "43"
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        "Calculating best minimal value for power law fit"
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        "\n",
        "44"
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        "Calculating best minimal value for power law fit"
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        "45"
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        "Calculating best minimal value for power law fit"
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        "46"
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        "47"
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        "Calculating best minimal value for power law fit"
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        "\n",
        "48"
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        "Calculating best minimal value for power law fit\n",
        "Calculating best minimal value for power law fit"
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       "text": [
        "\n",
        "49"
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        "Calculating best minimal value for power law fit"
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        "\n",
        "50"
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        "51"
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        "52"
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        "53"
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        "54"
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        "55"
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        "56"
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        "57"
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        "58"
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        "59"
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        "61"
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        "62"
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        "63"
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        "64"
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        "65"
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        "66"
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        "67"
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        "68"
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        "74"
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        "76"
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        "77"
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        "78"
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        "79"
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        "80"
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        "81"
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        "82"
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        "84"
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        "85"
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        "86"
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        "87"
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        "88"
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        "89"
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        "90"
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        "91"
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        "92"
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        "93"
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        "94"
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       "text": [
        "\n",
        "95"
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        "Calculating best minimal value for power law fit"
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       "text": [
        "\n",
        "96"
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        "\n",
        "Calculating best minimal value for power law fit"
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        "Calculating best minimal value for power law fit"
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        "Calculating best minimal value for power law fit"
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        "\n",
        "Calculating best minimal value for power law fit"
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       "text": [
        "\n",
        "97"
       ]
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       "text": [
        "\n",
        "Calculating best minimal value for power law fit"
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        "Calculating best minimal value for power law fit"
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        "Calculating best minimal value for power law fit"
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        "\n",
        "Calculating best minimal value for power law fit"
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        "Calculating best minimal value for power law fit"
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        "\n",
        "Calculating best minimal value for power law fit"
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       "text": [
        "\n",
        "98"
       ]
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        "\n",
        "Calculating best minimal value for power law fit"
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        "Calculating best minimal value for power law fit"
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        "Calculating best minimal value for power law fit"
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        "Calculating best minimal value for power law fit"
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        "Calculating best minimal value for power law fit"
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        "Calculating best minimal value for power law fit"
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        "\n",
        "Calculating best minimal value for power law fit"
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       "text": [
        "\n",
        "99"
       ]
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        "\n",
        "Calculating best minimal value for power law fit"
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        "Calculating best minimal value for power law fit"
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        "Calculating best minimal value for power law fit"
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        "Calculating best minimal value for power law fit"
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        "Calculating best minimal value for power law fit"
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       "text": [
        "\n",
        "100"
       ]
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        "\n",
        "Calculating best minimal value for power law fit"
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        "\n",
        "Calculating best minimal value for power law fit"
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        "Calculating best minimal value for power law fit"
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        "Calculating best minimal value for power law fit"
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        "\n",
        "Calculating best minimal value for power law fit"
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        "\n",
        "Calculating best minimal value for power law fit"
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        "\n",
        "Calculating best minimal value for power law fit"
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        "\n",
        "Calculating best minimal value for power law fit"
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       "text": [
        "\n",
        "101"
       ]
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        "\n",
        "Calculating best minimal value for power law fit"
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        "Calculating best minimal value for power law fit"
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        "Calculating best minimal value for power law fit"
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        "Calculating best minimal value for power law fit"
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        "Calculating best minimal value for power law fit"
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        "\n",
        "Calculating best minimal value for power law fit"
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        "Calculating best minimal value for power law fit"
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        "\n",
        "Calculating best minimal value for power law fit"
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       "text": [
        "\n",
        "102"
       ]
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        "\n",
        "Calculating best minimal value for power law fit"
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        "Calculating best minimal value for power law fit"
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        "Calculating best minimal value for power law fit"
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        "\n",
        "Calculating best minimal value for power law fit"
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        "\n",
        "Calculating best minimal value for power law fit"
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        "\n",
        "Calculating best minimal value for power law fit"
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      {
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        "\n",
        "Calculating best minimal value for power law fit"
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      {
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        "\n",
        "Calculating best minimal value for power law fit"
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      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "103"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Calculating best minimal value for power law fit"
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        "\n",
        "Calculating best minimal value for power law fit"
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        "Calculating best minimal value for power law fit"
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        "Calculating best minimal value for power law fit"
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        "Calculating best minimal value for power law fit"
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        "Calculating best minimal value for power law fit"
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        "\n",
        "Calculating best minimal value for power law fit"
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        "\n",
        "Calculating best minimal value for power law fit"
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      {
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        "\n",
        "Calculating best minimal value for power law fit"
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      {
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        "\n",
        "Calculating best minimal value for power law fit"
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      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "104"
       ]
      },
      {
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        "\n",
        "Calculating best minimal value for power law fit"
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        "Calculating best minimal value for power law fit"
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        "Calculating best minimal value for power law fit"
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        "Calculating best minimal value for power law fit"
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        "Calculating best minimal value for power law fit"
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        "\n",
        "Calculating best minimal value for power law fit"
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      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "105"
       ]
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      {
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       "text": [
        "\n",
        "Calculating best minimal value for power law fit"
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        "\n",
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        "Calculating best minimal value for power law fit"
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        "\n",
        "Calculating best minimal value for power law fit"
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      {
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        "\n",
        "Calculating best minimal value for power law fit"
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        "\n",
        "Calculating best minimal value for power law fit"
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      {
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        "\n",
        "Calculating best minimal value for power law fit"
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        "\n",
        "Calculating best minimal value for power law fit"
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      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "106"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Calculating best minimal value for power law fit"
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        "\n",
        "Calculating best minimal value for power law fit"
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        "Calculating best minimal value for power law fit"
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        "Calculating best minimal value for power law fit"
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        "Calculating best minimal value for power law fit"
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        "\n",
        "Calculating best minimal value for power law fit"
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      {
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        "\n",
        "Calculating best minimal value for power law fit"
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        "\n",
        "Calculating best minimal value for power law fit"
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      {
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        "\n",
        "Calculating best minimal value for power law fit"
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        "\n",
        "Calculating best minimal value for power law fit"
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      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "107"
       ]
      },
      {
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       "text": [
        "\n",
        "Calculating best minimal value for power law fit"
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        "Calculating best minimal value for power law fit"
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        "Calculating best minimal value for power law fit"
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        "Calculating best minimal value for power law fit"
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        "Calculating best minimal value for power law fit"
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       "text": [
        "\n",
        "Calculating best minimal value for power law fit"
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        "\n",
        "Calculating best minimal value for power law fit"
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       "text": [
        "\n",
        "Calculating best minimal value for power law fit"
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      {
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       "stream": "stdout",
       "text": [
        "\n",
        "Calculating best minimal value for power law fit"
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       "stream": "stdout",
       "text": [
        "\n",
        "Calculating best minimal value for power law fit"
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      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "108"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Calculating best minimal value for power law fit"
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        "\n",
        "Calculating best minimal value for power law fit"
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        "\n",
        "Calculating best minimal value for power law fit"
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        "\n",
        "Calculating best minimal value for power law fit"
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        "\n",
        "Calculating best minimal value for power law fit"
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        "\n",
        "Calculating best minimal value for power law fit"
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       "text": [
        "\n",
        "Calculating best minimal value for power law fit"
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       "text": [
        "\n",
        "Calculating best minimal value for power law fit"
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      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Calculating best minimal value for power law fit"
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      {
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       "stream": "stdout",
       "text": [
        "\n",
        "Calculating best minimal value for power law fit"
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      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "109"
       ]
      },
      {
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       "stream": "stdout",
       "text": [
        "\n",
        "Calculating best minimal value for power law fit"
       ]
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        "\n",
        "Calculating best minimal value for power law fit"
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        "\n",
        "Calculating best minimal value for power law fit"
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        "\n",
        "Calculating best minimal value for power law fit"
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        "\n",
        "Calculating best minimal value for power law fit"
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        "\n",
        "Calculating best minimal value for power law fit"
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       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Calculating best minimal value for power law fit"
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      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Calculating best minimal value for power law fit"
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      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Calculating best minimal value for power law fit"
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      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Calculating best minimal value for power law fit"
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      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "110"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Calculating best minimal value for power law fit"
       ]
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      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Calculating best minimal value for power law fit"
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       "text": [
        "\n",
        "Calculating best minimal value for power law fit"
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        "\n",
        "Calculating best minimal value for power law fit"
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        "\n",
        "Calculating best minimal value for power law fit"
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        "\n",
        "Calculating best minimal value for power law fit"
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       "text": [
        "\n",
        "Calculating best minimal value for power law fit"
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      {
       "output_type": "stream",
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       "text": [
        "\n",
        "Calculating best minimal value for power law fit"
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      {
       "output_type": "stream",
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       "text": [
        "\n",
        "Calculating best minimal value for power law fit"
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      {
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       "stream": "stdout",
       "text": [
        "\n",
        "Calculating best minimal value for power law fit"
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      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "111"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Calculating best minimal value for power law fit"
       ]
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      {
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        "\n",
        "Calculating best minimal value for power law fit"
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        "\n",
        "Calculating best minimal value for power law fit"
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        "\n",
        "Calculating best minimal value for power law fit"
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        "\n",
        "Calculating best minimal value for power law fit"
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        "\n",
        "Calculating best minimal value for power law fit"
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        "\n",
        "Calculating best minimal value for power law fit"
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      {
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       "text": [
        "\n",
        "Calculating best minimal value for power law fit"
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      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Calculating best minimal value for power law fit"
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      {
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       "text": [
        "\n",
        "Calculating best minimal value for power law fit"
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      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "112"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Calculating best minimal value for power law fit"
       ]
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      {
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        "\n",
        "Calculating best minimal value for power law fit"
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        "\n",
        "Calculating best minimal value for power law fit"
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        "\n",
        "Calculating best minimal value for power law fit"
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        "\n",
        "Calculating best minimal value for power law fit"
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        "\n",
        "Calculating best minimal value for power law fit"
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       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Calculating best minimal value for power law fit"
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      {
       "output_type": "stream",
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        "\n",
        "Calculating best minimal value for power law fit"
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      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Calculating best minimal value for power law fit"
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      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Calculating best minimal value for power law fit"
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      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "113"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Calculating best minimal value for power law fit"
       ]
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      {
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        "\n",
        "Calculating best minimal value for power law fit"
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        "\n",
        "Calculating best minimal value for power law fit"
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        "\n",
        "Calculating best minimal value for power law fit"
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        "\n",
        "Calculating best minimal value for power law fit"
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        "\n",
        "Calculating best minimal value for power law fit"
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      {
       "output_type": "stream",
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        "\n",
        "Calculating best minimal value for power law fit"
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      {
       "output_type": "stream",
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       "text": [
        "\n",
        "Calculating best minimal value for power law fit"
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      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Calculating best minimal value for power law fit"
       ]
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      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Calculating best minimal value for power law fit"
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      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "114"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Calculating best minimal value for power law fit"
       ]
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      {
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        "\n",
        "Calculating best minimal value for power law fit"
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        "\n",
        "Calculating best minimal value for power law fit"
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        "\n",
        "Calculating best minimal value for power law fit"
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        "\n",
        "Calculating best minimal value for power law fit"
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        "\n",
        "Calculating best minimal value for power law fit"
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      {
       "output_type": "stream",
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        "\n",
        "Calculating best minimal value for power law fit"
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      {
       "output_type": "stream",
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       "text": [
        "\n",
        "Calculating best minimal value for power law fit"
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      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Calculating best minimal value for power law fit"
       ]
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      {
       "output_type": "stream",
       "stream": "stdout",
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        "\n",
        "Calculating best minimal value for power law fit"
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      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "115"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Calculating best minimal value for power law fit"
       ]
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      {
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        "\n",
        "Calculating best minimal value for power law fit"
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        "\n",
        "Calculating best minimal value for power law fit"
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        "\n",
        "Calculating best minimal value for power law fit"
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        "\n",
        "Calculating best minimal value for power law fit"
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        "\n",
        "Calculating best minimal value for power law fit"
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       "output_type": "stream",
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        "\n",
        "Calculating best minimal value for power law fit"
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      {
       "output_type": "stream",
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        "\n",
        "Calculating best minimal value for power law fit"
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      {
       "output_type": "stream",
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       "text": [
        "\n",
        "Calculating best minimal value for power law fit"
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      {
       "output_type": "stream",
       "stream": "stdout",
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        "\n",
        "Calculating best minimal value for power law fit"
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      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "116"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Calculating best minimal value for power law fit"
       ]
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      {
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        "\n",
        "Calculating best minimal value for power law fit"
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        "\n",
        "Calculating best minimal value for power law fit"
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        "\n",
        "Calculating best minimal value for power law fit"
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        "\n",
        "Calculating best minimal value for power law fit"
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        "\n",
        "Calculating best minimal value for power law fit"
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       "output_type": "stream",
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        "\n",
        "Calculating best minimal value for power law fit"
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       "output_type": "stream",
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        "\n",
        "Calculating best minimal value for power law fit"
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      {
       "output_type": "stream",
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        "\n",
        "Calculating best minimal value for power law fit"
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      {
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        "\n",
        "Calculating best minimal value for power law fit"
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      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "117"
       ]
      },
      {
       "output_type": "stream",
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       "text": [
        "\n",
        "Calculating best minimal value for power law fit"
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        "\n",
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        "Calculating best minimal value for power law fit"
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        "\n",
        "Calculating best minimal value for power law fit"
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        "\n",
        "Calculating best minimal value for power law fit"
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      {
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        "\n",
        "Calculating best minimal value for power law fit"
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        "\n",
        "Calculating best minimal value for power law fit"
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      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "118"
       ]
      },
      {
       "output_type": "stream",
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       "text": [
        "\n",
        "Calculating best minimal value for power law fit"
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        "\n",
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        "Calculating best minimal value for power law fit"
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        "Calculating best minimal value for power law fit"
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        "\n",
        "Calculating best minimal value for power law fit"
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        "\n",
        "Calculating best minimal value for power law fit"
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        "\n",
        "Calculating best minimal value for power law fit"
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      {
       "output_type": "stream",
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        "\n",
        "Calculating best minimal value for power law fit"
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      {
       "output_type": "stream",
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        "\n",
        "Calculating best minimal value for power law fit"
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      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "119"
       ]
      },
      {
       "output_type": "stream",
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       "text": [
        "\n",
        "Calculating best minimal value for power law fit"
       ]
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        "\n",
        "Calculating best minimal value for power law fit"
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        "\n",
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        "Calculating best minimal value for power law fit"
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        "\n",
        "Calculating best minimal value for power law fit"
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        "\n",
        "Calculating best minimal value for power law fit"
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      {
       "output_type": "stream",
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        "\n",
        "Calculating best minimal value for power law fit"
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      {
       "output_type": "stream",
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        "\n",
        "Calculating best minimal value for power law fit"
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      {
       "output_type": "stream",
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        "\n",
        "Calculating best minimal value for power law fit"
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      {
       "output_type": "stream",
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       "text": [
        "\n",
        "Calculating best minimal value for power law fit"
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      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "120"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Calculating best minimal value for power law fit"
       ]
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      {
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        "\n",
        "Calculating best minimal value for power law fit"
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        "\n",
        "Calculating best minimal value for power law fit"
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        "121"
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        "122"
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        "\n",
        "123"
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        "\n",
        "124"
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        "\n",
        "125"
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        "126"
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        "\n",
        "127"
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        "\n",
        "128"
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        "\n",
        "129"
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        "130"
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        "\n",
        "131"
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        "\n",
        "132"
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       "text": [
        "\n",
        "133"
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        "Calculating best minimal value for power law fit"
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        "\n",
        "134"
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        "Calculating best minimal value for power law fit"
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       "text": [
        "\n",
        "135"
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        "Calculating best minimal value for power law fit"
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        "Calculating best minimal value for power law fit"
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        "\n",
        "Calculating best minimal value for power law fit"
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        "Calculating best minimal value for power law fit"
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        "\n",
        "Calculating best minimal value for power law fit"
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       "text": [
        "\n",
        "136"
       ]
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        "Calculating best minimal value for power law fit"
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        "Calculating best minimal value for power law fit"
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        "Calculating best minimal value for power law fit"
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        "Calculating best minimal value for power law fit"
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        "\n",
        "Calculating best minimal value for power law fit"
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       "text": [
        "\n",
        "137"
       ]
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        "\n",
        "Calculating best minimal value for power law fit"
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        "Calculating best minimal value for power law fit"
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        "Calculating best minimal value for power law fit"
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        "\n",
        "Calculating best minimal value for power law fit"
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       "text": [
        "\n",
        "138"
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        "Calculating best minimal value for power law fit"
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        "Calculating best minimal value for power law fit"
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        "Calculating best minimal value for power law fit"
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        "\n",
        "Calculating best minimal value for power law fit"
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       "text": [
        "\n",
        "139"
       ]
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        "\n",
        "Calculating best minimal value for power law fit"
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        "Calculating best minimal value for power law fit"
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        "Calculating best minimal value for power law fit"
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        "\n",
        "Calculating best minimal value for power law fit"
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       "text": [
        "\n",
        "140"
       ]
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        "\n",
        "Calculating best minimal value for power law fit"
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        "\n",
        "Calculating best minimal value for power law fit"
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        "Calculating best minimal value for power law fit"
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        "\n",
        "Calculating best minimal value for power law fit"
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       "text": [
        "\n",
        "141"
       ]
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        "\n",
        "Calculating best minimal value for power law fit"
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       "text": [
        "\n",
        "142"
       ]
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        "\n",
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       "text": [
        "\n",
        "143"
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        "\n",
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       "text": [
        "\n",
        "144"
       ]
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        "\n",
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        "\n",
        "145"
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        "146"
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        "147"
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        "148"
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        "149"
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        "150"
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        "151"
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        "152"
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        "153"
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        "154"
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        "156"
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        "157"
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        "158"
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        "159"
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        "160"
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        "161"
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        "164"
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        "166"
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        "168"
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        "169"
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        "\n",
        "170"
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        "\n",
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        "\n",
        "Calculating best minimal value for power law fit"
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        "Calculating best minimal value for power law fit"
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      {
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        "\n"
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     ],
     "prompt_number": 182
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#filename = 'powerlaw_validation_%itrials_%idata.h5'%(int(n_trials),int(n_data))\n",
      "#df = pd.read_hdf(filename,'df')"
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     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 40
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "subplot(2,2,1)\n",
      "for a in theoretical_alphas:\n",
      "    y_vals = df.ix['continuous', a]['alpha_mean']\n",
      "    error = df.ix['continuous', a]['alpha_sd']\n",
      "\n",
      "    plot(theoretical_xmins, y_vals, label=a)\n",
      "    fill_between(theoretical_xmins, y_vals-error, y_vals+error, alpha=.1)\n",
      "\n",
      "xscale('log')\n",
      "#xlabel(r\"$x_{min}$\")\n",
      "ylabel(r\"Fitted $\\alpha$\")\n",
      "yticks(theoretical_alphas)\n",
      "setp(gca().get_xticklabels(), visible=False)\n",
      "title(\"Continuous\")\n",
      "\n",
      "#########\n",
      "subplot(2,2,2)\n",
      "for a in theoretical_alphas:\n",
      "    y_vals = df.ix['discrete', a]['alpha_mean']\n",
      "    error = df.ix['discrete', a]['alpha_sd']\n",
      "\n",
      "    plot(theoretical_xmins, y_vals, label=a)\n",
      "    fill_between(theoretical_xmins, y_vals-error, y_vals+error, alpha=.1)\n",
      "\n",
      "xscale('log')\n",
      "#xlabel(r\"$x_{min}$\")\n",
      "#ylabel(r\"Fitted $\\alpha$\")\n",
      "setp(gca().get_xticklabels(), visible=False)\n",
      "setp(gca().get_yticklabels(), visible=False)\n",
      "title(\"Discrete\")\n",
      "\n",
      "########\n",
      "subplot(2,2,3)\n",
      "for a in theoretical_alphas:\n",
      "    y_vals = df.ix['continuous', a]['xmin_mean']\n",
      "    error = df.ix['continuous', a]['xmin_sd']\n",
      "    up = y_vals+error\n",
      "    down = y_vals-error\n",
      "    ind = down<theoretical_xmins\n",
      "    down[ind] = theoretical_xmins[ind]\n",
      "    \n",
      "    plot(theoretical_xmins, y_vals, label=a)\n",
      "    fill_between(theoretical_xmins, down, up, alpha=.1)\n",
      "\n",
      "xlim(xmin=1)\n",
      "ylim(ymin=1)\n",
      "plot(xlim(),xlim(),linestyle='--', color='k')\n",
      "xscale('log')\n",
      "yscale('log')\n",
      "xlabel(r\"$x_{min}$ of Data\")\n",
      "ylabel(r\"Fitted $x_{min}$\")\n",
      "\n",
      "\n",
      "########\n",
      "legend_refs = []\n",
      "########\n",
      "subplot(2,2,4,sharey=gca())\n",
      "for a in theoretical_alphas:\n",
      "    y_vals = df.ix['discrete', a]['xmin_mean']\n",
      "    error = df.ix['discrete', a]['xmin_sd']\n",
      "    up = y_vals+error\n",
      "    down = y_vals-error\n",
      "    ind = down<theoretical_xmins\n",
      "    down[ind] = theoretical_xmins[ind]\n",
      "\n",
      "    line = plot(theoretical_xmins, y_vals, label=a)\n",
      "    legend_refs += line\n",
      "    fill_between(theoretical_xmins, down, up, alpha=.1)\n",
      "\n",
      "xlim(xmin=1)\n",
      "ylim(ymin=1)\n",
      "plot(xlim(),xlim(),linestyle='--', color='k')\n",
      "xscale('log')\n",
      "yscale('log')\n",
      "xlabel(r\"$x_{min}$ of Data\")\n",
      "#ylabel(r\"Fitted $x_{min}$\")\n",
      "setp(gca().get_yticklabels(), visible=False)\n",
      "\n",
      "\n",
      "#######\n",
      "#figlegend(legend_refs[::-1], theoretical_alphas[::-1],'center right', title=r'$\\alpha$ of Data')\n",
      "subplots_adjust(wspace=.15, hspace=.1)\n",
      "legend( legend_refs[::-1], theoretical_alphas[::-1], loc = 'center right', bbox_to_anchor = (.1,0,1,1),\n",
      "            bbox_transform = plt.gcf().transFigure, title=r'$\\alpha$ of Data' )\n",
      "savefig('Fig_powerlaw_validation_%itrials_%idata.pdf'%(int(n_trials),int(n_data)), bbox_inches='tight')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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CDkXSm3Lm1nvnZwe6vqYffMCAppdLIZmHju/UxaiLg+hY2g2Xdbur787u3Hdb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\nS4rK2lsM72V/azIMl/GzlY1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dFfv8zFUQBEEQdsWOHTt4/vnnOeOMM3Bdl+XLl/PKK6/w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      }
     ],
     "prompt_number": 41
    }
   ],
   "metadata": {}
  }
 ]
}